Regularity Conditions for Concave Programming in Finite Dimensional Spaces.

Constrained maximum problems with finitely many variables and finitely many constraints are examined with the assumption that the objective and the constraint functions are concave but not necessarily differentiable. A regularity condition necessary and sufficient for a maximum to be attained and for the problems to be reducible to saddle-point problems is presented. Further, a constraint qualification sufficient for the problems to be regular for any concave objective function is presented, of which Slater-Uzawas constraint qualifications are special cases. Author